Modeling mask corner rounding effects using multiple mask layers

ABSTRACT

An embodiment provides systems and techniques for determining an improved process model which models mask corner rounding (MCR) effects. During operation, the system may receive a mask layout and process data which was generated by applying a photolithography process to the mask layout. The system may also receive an uncalibrated process model which may contain a set of MCR components. Next, the system may identify a set of corners in the mask layout. The system may then determine a set of mask layers, wherein at least some of the mask layers correspond to the MCR components. Next, the system may determine an improved process model by calibrating the uncalibrated process model using the set of mask layers, and the process data.

RELATED APPLICATION

This application is a divisional application of U.S. application Ser.No. 11/863,624, Attorney Docket Number SNPS-1008, entitled “FacilitatingProcess Model Accuracy by Modeling Mask Corner Rounding Effects,” byinventors Jensheng Huang, Chun-chieh Kuo, Lawrence S. Melvin III, filedon 28 Sep. 2007.

BACKGROUND

1. Field of the Invention

The present invention relates to semiconductor design and manufacturing.More specifically, the present invention relates to improving processmodel accuracy by modeling mask corner rounding (MCR) effects.

2. Related Art

Rapid advances in computing technology have made it possible to performtrillions of computational operations each second on data sets that aresometimes as large as trillions of bytes. These advances can beattributed to the dramatic improvements in semiconductor manufacturingtechnologies which have made it possible to integrate tens of millionsof devices onto a single chip.

Semiconductor manufacturing technologies typically include a number ofprocesses which involve complex physical and chemical interactions.Since it is almost impossible to find exact formulae to predict thebehavior of these complex interactions, researchers typically useprocess models which are fit to empirical data to predict the behaviorof these processes. A process model can be used in a number ofapplications during the design of a semiconductor chip. For example,process models are commonly used for making corrections to layouts tocompensate for undesirable effects of semiconductor manufacturingprocesses.

Inaccuracies in the process model can negatively affect the efficacy ofdownstream applications. For example, inaccuracies in the process modelcan reduce the efficacy of optical proximity correction (OPC). Assemiconductor integration densities continue to increase at anexponential rate, the accuracy of process models is becomingincreasingly important. Hence, it is desirable to improve process modelaccuracy.

SUMMARY

Embodiments of the present invention provide systems and techniques fordetermining an improved process model which models mask corner roundingeffects. A process model is usually determined by fitting or calibratingkernel coefficients to process data. The process data is usuallygenerated by applying the semiconductor manufacturing processes that arebeing modeled to a mask layout.

An embodiment of the present invention can modify a mask layout inproximity to a set of corners, and use the modified mask layout duringprocess model calibration. Alternatively, an embodiment can determine aset of mask layers. One of the mask layers may be the mask layout itselfor it may contain substantially all of the patterns in the mask layout.Other mask layers may contain patterns that relate to corners in themask layout. The embodiment may calibrate the process model using theset of mask layers.

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 illustrates various steps in the design and fabrication of anintegrated circuit in accordance with an embodiment of the presentinvention.

FIG. 2 illustrates a typical optical system in accordance with anembodiment of the present invention.

FIG. 3A illustrates a portion of a mask layout in accordance with anembodiment of the present invention.

FIG. 3B illustrates a photolithography mask in accordance with anembodiment of the present invention.

FIG. 4 presents a flowchart that illustrates a single-layer approach fordetermining a process model that models MCR effects in accordance withan embodiment of the present invention.

FIG. 5A illustrates a set of corners in the mask layout in accordancewith an embodiment of the present invention.

FIGS. 5B-5F illustrate how a mask layout can be modified in proximity toa set of corners in accordance with an embodiment of the presentinvention.

FIG. 6 presents a flowchart that illustrates a multi-layer approach fordetermining a process model that models MCR effects in accordance withan embodiment of the present invention.

FIGS. 7A and 7B illustrate a set of mask layers in accordance with anembodiment of the present invention.

FIG. 8A illustrates an outer corner mask layer in accordance with anembodiment of the present invention.

FIG. 8B illustrates an inner corner mask layer in accordance with anembodiment of the present invention.

FIG. 9 presents a flowchart that illustrates a process for determiningan improved process model in accordance with an embodiment of thepresent invention.

FIG. 10 illustrates a computer system in accordance with an embodimentof the present invention.

FIG. 11 illustrates how a process model can be stored in accordance withan embodiment of the present invention.

DETAILED DESCRIPTION Integrated Circuit (IC) Design Flow

FIG. 1 illustrates various steps in the design and fabrication of anintegrated circuit in accordance with an embodiment of the presentinvention.

The process usually starts with a product idea (step 100) which isrealized using an EDA software design process (step 110). Once thedesign is finalized, it is usually taped-out (event 140) and goesthrough the fabrication process (step 150) and packaging and assemblyprocesses (step 160) to produce the finished chips (result 170).

The EDA software design process (step 110) comprises steps 112-130,which are described below for illustration purposes only and are notmeant to limit the present invention. For example, an actual integratedcircuit design may require the designer to perform the design steps in adifferent sequence than the sequence described below.

System design (step 112): In this step, the designers describe thefunctionality that they want to implement. They can also perform what-ifplanning to refine functionality, check costs, etc. Hardware-softwarearchitecture partitioning can occur at this stage. Exemplary EDAsoftware products from Synopsys, Inc. that can be used at this stepinclude Model Architect, Saber®, System Studio, and DesignWare®products.

Logic design and functional verification (step 114): At this stage, theVHDL or Verilog code for modules in the system is written and the designis checked for functional accuracy. More specifically, the design ischecked to ensure that it produces the correct outputs. Exemplary EDAsoftware products from Synopsys, Inc. that can be used at this stepinclude VCS®, Vera®, DesignWare®, Magellan™, Formality®, ESP and Leda®products.

Synthesis and design for test (step 116): Here, the VHDL/Verilog istranslated to a netlist. The netlist can be optimized for the targettechnology. Additionally, tests can be designed and implemented to checkthe finished chips. Exemplary EDA software products from Synopsys, Inc.that can be used at this step include Design Compiler®, PhysicalCompiler®, Test Compiler, Power Compiler™, FPGA Compiler, TetraMAX®, andDesignWare® products.

Netlist verification (step 118): In this step, the netlist is checkedfor compliance with timing constraints and for correspondence with theVHDL/Verilog source code. Exemplary EDA software products from Synopsys,Inc. that can be used at this step include Formality®, PrimeTime®, andVCS® products.

Design planning (step 120): Here, an overall floorplan for the chip isconstructed and analyzed for timing and top-level routing. Exemplary EDAsoftware products from Synopsys, Inc. that can be used at this stepinclude Astro™ and IC Compiler products.

Physical implementation (step 122): The placement (positioning ofcircuit elements) and routing (connection of the same) occurs at thisstep. Exemplary EDA software products from Synopsys, Inc. that can beused at this step include the Astro™ and IC Compiler products.

Analysis and extraction (step 124): At this stage, the circuit functionis verified at a transistor level, this in turn permits what-ifrefinement. Exemplary EDA software products from Synopsys, Inc. that canbe used at this step include AstroRail™, PrimeRail, PrimeTime®, andStar-RCXTT™ products.

Physical verification (step 126): In this step, the design is checked toensure correctness for manufacturing, electrical issues, lithographicissues, and circuitry. Exemplary EDA software products from Synopsys,Inc. that can be used at this step include the Hercules™ product.

Resolution enhancement (step 128): This step involves geometricmanipulations of the layout to improve manufacturability of the design.Exemplary EDA software products from Synopsys, Inc. that can be used atthis step include Proteus/Progen, ProteusAF, and PSMGen products.

Mask data preparation (step 130): This step provides the “tape-out” datafor production of masks to produce finished chips. Exemplary EDAsoftware products from Synopsys, Inc. that can be used at this stepinclude the CATS® family of products.

Embodiments of the present invention can be used during one or more ofthe above-described steps. Specifically, one embodiment of the presentinvention can be used during the resolution enhancement step 128.

Process Models

A process model models the behavior of one or more semiconductormanufacturing processes which typically involve complex physical andchemical interactions. A process model is usually determined by fittingor calibrating kernel coefficients to empirical data. The empirical datais usually generated by applying the semiconductor manufacturingprocesses that are being modeled to one or more test layouts. Forexample, a photolithography process can be used to print a test layouton a wafer. Next, the empirical data can be obtained by measuring thecritical dimensions (CD) of the features on the wafer before and/orafter the etch process. The process model can then be fit to theempirical data to determine a process model that models thephotolithography process.

Once a process model is determined, it can be used in a number ofapplications during the design and manufacture of a semiconductor chip.For example, process models are typically used to support OpticalProximity Correction (OPC) and Resolution Enhancement Techniques (RET).These models can allow full-chip database manipulation in reasonabletimeframes during the tapeout flow.

An uncalibrated process model typically includes components that areassociated with parameters and/or coefficients. During calibration, theparameters and/or coefficients can be statistically fit to empiricaldata to obtain the final process model. A component in the process modelis typically a mathematical expression that is designed to model aparticular physical effect. For example, a process model may berepresented as

${\sum\limits_{i}\left( {C_{i} \cdot K_{i}} \right)},$

where K_(i) is a component or kernel, and C_(i) is a coefficient whichis associated with K_(i). The empirical data may include values of adesired property, e.g., the CD, at different locations in the layout.Once the process model is fit to the empirical data, it can then be usedto predict the value of the desired property for other layouts.

It is usually impossible to calibrate coefficient values so that thepredicted data exactly matches the empirical data. Even if an exact fitwas available, it may not be desirable because the resulting processmodel may not interpolate and/or extrapolate properly. Typically,statistical fitting techniques are used to determine the parametersand/or coefficients so that the error between the empirical data and thepredicted data is minimized. In one embodiment, the system can use aleast-squares fitting technique to determine the parameter and/orcoefficient values.

A process model is considered to be robust if it interpolates andextrapolates well, i.e., if the process model generates accurate resultswhen it is applied to layouts that are different from the layouts thatwere used during the fitting process. In general, the fewer modelingfunctions or kernels that a process model uses, the more robust it is.However, using fewer kernels may decrease the process model's accuracy.Hence, there is usually a tradeoff between the robustness and theaccuracy of a process model.

Photolithography Process Models

The optical model in a photolithography process model is usually basedon the Hopkins model which models the behavior of partially coherentoptical systems.

FIG. 2 illustrates a typical optical system in accordance with anembodiment of the present invention.

Radiation from source 202 can be collimated by a condenser 204.

The collimated light can then pass through mask 206, aperture 208, lensbody 210, and form an image on a wafer 212.

Hopkins model can be described using the expression:

I(x,y)=∫∫∫∫J(x′,y′;x″,y″)

L(x,y;x′,y′)

L*(x,y;x″,y″)dx′dy′ dx″ dy″,

where, I(x, y) is the optical intensity at point (x, y) on the wafer,L(x, y; x′, y′) is a lumped model of the light source and the mask, L*is the complex conjugate of L, and J(x′, y′; x″, y″) models theincoherence between two points of light on the mask. The lumped model(L) essentially treats the mask as an array of light sources. Inparticular, L(x, y; x′, y′) models point (x′, y′) on the mask as a pointsource, and J(x′, y′; x″, y″) models the incoherence between the lightemanating from points (x′, y′) and (x″, y″) on the mask. The lumpedmodel (L) can be represented as a convolution between the mask and thesource. For example, the lumped model can be represented using a maskmodel and a source model as follows:

L(x,y;x′,y′)=M(x′,y′)

K(x,y;x′,y′),

where M(x′, y′) models the mask and K(x, y; x′, y′) models the source.

The Hopkins model can be used to determine a 4-D (four dimensional)matrix called the Transmission Cross Coefficient (TCC) matrix whichmodels the optical system. The TCC matrix can then be represented usinga set of orthogonal 2-D (two dimensional) kernels. The set of orthogonalkernels can be determined using the eigenfunctions of the TCC matrix.The features on the wafer can be determined by convolving the set of 2-Dkernels with the mask. General information on photolithography andprocess modeling can be found in Alfred Kwok-Kit Wong, Optical Imagingin Projection Microlithography, SPIE-International Society for OpticalEngine, 2005, and Grant R. Fowles, Introduction to Modern Optics, 2^(nd)Edition, Dover Publications, 1989.

In one embodiment, the system uses a set of orthogonal functions calledZernike polynomials to represent the optical system. Zernike polynomialsare made up of terms that are of the same form as the types ofaberrations often observed in optical systems. For example, one Zernikepolynomial may be associated with defocus, while another may beassociated with tilt, etc. The optical system can be represented usingthe expression

${\sum\limits_{i}\left( {C_{i} \cdot Z_{i}} \right)},$

where Z_(i) is a Zernike polynomial and C_(i) is an optical coefficientwhich is associated with Z_(i). In one embodiment, the system may modifythe coefficients in the optical model so that the optical model alsomodels MCR effects. Alternatively, the system may add additional kernelsor components to the optical model to capture the MCR effects.

Modeling Mask Corner Rounding Effects

Process model accuracy has become very important at currentsemiconductor integration densities, and is expected to become even moreimportant in the future. Since conventional process models are notaccurate enough at current integration densities, there is a strong needto improve process model accuracy.

Process models are usually based on a physical model or a black-boxmodel, or a combination thereof. A physical model models the underlyingphysical process, whereas a black-box model typically uses genericmodeling functions. The physical modeling approach is generallypreferred because the black-box modeling approach can have a number ofdrawbacks. First, the generic modeling functions that are used in ablack-box model usually require a large amount of empirical data toconverge. Second, black-box models are not as accurate as physicalmodels. Specifically, a black-box model is fit to empirical data whichis obtained using a test layout. However, this does not guarantee thatthe model will work accurately with other layouts. Third, the empiricaldata is usually obtained at a particular process point (i.e., undercertain process conditions). Hence, a black-box model that is fit toempirical data for a particular process point may not work accuratelyunder different process conditions, e.g., under defocus or a differentexposure energy. Hence, it is generally desirable to use physical modelsinstead of black-box models.

However, determining an appropriate physical model is very challenging.In a typical physical modeling approach, first we have to identify asystematic process variation that is not negligible and which has notbeen modeled by the process model. Next, we have to identify theunderlying physical processes which are causing the systematicvariation. Finally, we have to determine a model that accurately modelsthe underlying physical processes without sacrificing runtimeperformance.

At current integration densities, mask corner rounding (MCR) effects arecausing non-negligible systematic process variations. Conventionalprocess models do not accurately model these effects because they eithercompletely ignore them, or they try to model the effects using black-boxmodeling techniques which do not accurately capture the underlyingphysical processes. In contrast to conventional techniques, oneembodiment of the present invention accurately models MCR effects bydetermining an appropriate physical model.

FIG. 3A illustrates a portion of a mask layout in accordance with anembodiment of the present invention.

Polygon 302 is part of a mask layout and has an inner corner 304 and anouter corner 306. An inner corner is a corner whose interior angle isgreater than 180°. For example, the interior angle 308 of inner corner304 is greater than 180°. Conversely, an outer corner is a corner whoseinterior angle is less than 180°. For example, the interior angle 310 ofouter corner 306 is less than 180°.

FIG. 3B illustrates a photolithography mask in accordance with anembodiment of the present invention.

A photolithography mask is typically fabricated using electron beamlithography. Shapes in the mask layout are usually not transferredperfectly onto the photolithography mask. Specifically, sharp angles inthe mask layout may become “rounded” during mask fabrication. Thiseffect is known has “mask corner rounding.” For example, when polygon302 shown in FIG. 3A is fabricated, it may create polygon 352 shown inFIG. 3B. MCR effects may cause corners 304 and 306 in the mask layoutshown in FIG. 3A to produce rounded corners 354 and 356, respectively,in the photolithography mask shown in FIG. 3B.

Conventional process models typically predict the shapes on the waferusing a mask layout which contains “perfect” polygons, e.g., polygon302. However, since the actual polygons on the photolithography mask arenot “perfect,” e.g., polygon 352, the results produced by conventionalmodels are inaccurate. Conventional approaches that use black-box modelsto model corner rounding effects may not be successful because black-boxmodels may not accurately capture the underlying physical processes thataffect different types of corners in different ways. For example, theMCR effect on inner corners and outer corners may be different, and thisdifference may not be properly captured by a black-box model.Furthermore, conventional approaches that model MCR effects using ablack-box model can cause the process model to become inaccurate forother types of patterns, e.g., line-and-space patterns.

Modeling approaches used in the present invention do not suffer from theabove-described drawbacks because they model the MCR effects based onthe underlying physical processes. The following sections describeapproaches for modeling MCR effects in accordance with embodiments ofthe present invention.

Single-Layer Approach

FIG. 4 presents a flowchart that illustrates a single-layer approach fordetermining a process model that models MCR effects in accordance withan embodiment of the present invention.

In the single-layer approach, the process can begin by receiving a masklayout (step 402). Note that a mask layout typically contains perfectlyshaped polygons that do not represent the effects of MCR.

Next, the system can receive process data which was generated byapplying a photolithography process to the mask layout (step 404). Theprocess data may be generated by measuring critical dimensions offeatures that were produced when the mask layout was subjected to thesemiconductor manufacturing processes that are being modeled.

The system can then receive an uncalibrated process model (step 406).The uncalibrated process model can typically be represented as

${\sum\limits_{i}\left( {C_{i} \cdot K_{i}} \right)},$

where K_(i) is a component or kernel, and C_(i) is a coefficient whichis associated with K_(i). In an “uncalibrated” process model, thecoefficients C_(i) are usually unknown.

Next, the system can identify a set of corners in the mask layout (step408).

FIG. 5A illustrates a set of corners in the mask layout in accordancewith an embodiment of the present invention.

Polygon 502 is part of a mask layout. The system may identify all thecorners in the mask layout or it may identify only some of the corners.For example, the system may identify corners 504, 506, 508, 510, 512,and 514. Further, the system may categorize the corners in a mask layoutbased on their shape, size, location, or any other characteristic thatmay affect the amount or the intensity of the MCR effect. In oneembodiment, the system categorizes corners into two types: inner cornersand outer corners. For example, the system may categorize corners 504,506, 510, 512, and 514 as outer corners, and corner 508 as an innercorner.

The system can then modify the mask layout in proximity to the set ofcorners to obtain a modified mask layout (step 410). Although themodifications to the mask layout may relate to the MCR effects, theshapes and sizes of the modifications may not directly correspond to theactual shapes and sizes that are produced by mask corner rounding. Oneembodiment treats the shapes and sizes of the modifications asparameters that are fit to process data.

FIGS. 5B-5F illustrate how a mask layout can be modified in proximity toa set of corners in accordance with an embodiment of the presentinvention.

The system can modify the mask layout by adding a bevel artifact to acorner in the set of corners. FIG. 5B illustrates how the system can addbevel artifacts 522 and 524 to outer corner 504 and inner corner 508,respectively. Although FIG. 5B shows that bevel artifacts were added toall the corners of the polygon, the system may add a bevel artifact toonly some of the corners of a polygon. The size of the bevel artifactmay not directly correspond to the actual amount of rounding that occursduring mask fabrication. Specifically, one embodiment empiricallydetermines the bevel size that maximally improves process modelaccuracy.

Note that adding a bevel artifact to an outer corner usually cuts intothe polygon, e.g., bevel artifact 522, whereas adding a bevel artifactto an inner corner usually increases the area of the polygon, e.g.,bevel artifact 524. One embodiment of the present invention directlymodels this difference between inner and outer corners because itmodifies the mask layout differently in proximity to inner and outercorners. In contrast, conventional approaches that use black-boxmodeling may not be able to capture this difference.

Instead of adding a bevel artifact, the system can add a notch artifact.FIG. 5C illustrates how the system can add notch artifacts 532 and 534to outer corner 504 and inner corner 508, respectively. Just like bevelartifacts, adding a notch artifact to an outer corner usually cuts intothe polygon, e.g., notch artifact 532, whereas adding a notch artifactto an inner corner usually increases the area of the polygon, e.g.,notch artifact 534. Although FIG. 5C shows that notch artifacts wereadded to all the corners of the polygon, the system may add a notchartifact to only some of the corners of a polygon. Further, just likebevel artifacts, an embodiment may empirically determine the notch sizethat maximally improves process model accuracy.

The system may add different types of artifacts to different types ofcorners. In particular, the system may add different types of artifactsto inner and outer corners. For example, the system can add differentsized notches to inner and outer corners. FIG. 5D illustrates how thesystem can add a larger notch to outer corners, e.g., notch 542, and asmaller notch to inner corners, e.g., notch 544. FIG. 5E illustrates howthe system can add a notch artifact to only outer corners, e.g., notch552, and not add any notches to inner corner, e.g., corner 508.

Alternatively, the system may add a notch to an inner corner and a bevelto an outer corner, or vice versa. These artifacts and modificationtechniques have been presented for illustration purposes and are notintended to limit the present invention. Many modifications andvariations will be readily apparent to practitioners skilled in the art.For example, FIG. 5F illustrates how the system may add notches to somecorners, e.g., notch 562, bevels to some corners, e.g., bevel 564, andmay not add any artifacts to some corners, e.g., corner 508.

Next, the system can determine the improved process model by calibratingthe uncalibrated process model using the modified mask layout and theprocess data (step 412).

Specifically, the system can determine the process model by fittingcoefficients in the uncalibrated process model using the process data.The fitting process can include convolving the kernels in theuncalibrated process model with the modified mask layout. For example,one embodiment can use a least square fitting technique to calibrate theprocess model. Specifically, coefficients C_(j) in the uncalibratedprocess model

${\sum\limits_{j = 1}^{m}\left( {C_{j} \cdot K_{j}} \right)},$

can be determined by solving for a least square fit as follows:

${{\begin{pmatrix}{M_{1} \otimes K_{1}} & \ldots & {M_{1} \otimes K_{m}} \\\vdots & \ddots & \vdots \\{M_{n} \otimes K_{1}} & \ldots & {M_{n} \otimes K_{m}}\end{pmatrix} \cdot \begin{pmatrix}C_{1} \\\vdots \\C_{m}\end{pmatrix}} \approx \begin{pmatrix}d_{1} \\\vdots \\d_{n}\end{pmatrix}},$

where M_(i)

K_(j) is the convolution of the mask layout with kernel K_(j) at samplepoint i, and d_(i) is the empirical process data at sample point i. Notethat the above equation indicates that the two sides of the equation maybe approximately equal to one another. This is because it may beimpossible to determine a set of coefficients that exactly satisfies theequation. However, when such a set of coefficients exist, the“approximately equal” sign in the equation should be interpreted as anequality sign.

Multi-Layer Approach

FIG. 6 presents a flowchart that illustrates a multi-layer approach fordetermining a process model that models MCR effects in accordance withan embodiment of the present invention.

As in the single-layer approach, the multi-layer approach can begin byreceiving a mask layout (step 602), and receive process data which wasgenerated by applying a photolithography process to the mask layout(step 604).

Next, the system can receive an uncalibrated process model which caninclude an optical component and a set of mask-corner-rounding (MCR)components (step 606). The set of MCR components can include one or moreMCR components that are designed to model MCR effects. Note that thephrase “a set of MCR components,” as used here, does not necessarilyimply that the set has a plurality of MCR components. Specifically, inone embodiment, the set may contain only one MCR component.

For example, the uncalibrated process model may be expressed as:

${{\sum\limits_{i = 1}^{m}\left( {C_{i} \cdot K_{i}} \right)} + {\sum\limits_{j = 1}^{n}X_{j}}},$

where

$\sum\limits_{i}\left( {C_{i} \cdot K_{i}} \right)$

represents an optical component with m kernels, and X_(j) represents thej^(th) MCR component. Each MCR component can comprise one or morekernels, e.g.,

${X_{j} = {\sum\limits_{k = 1}^{n}\left( {C_{k}^{j} \cdot K_{k}^{j}} \right)}},$

where C_(k) ^(j) is the k^(th) coefficient in the j^(th) MCR component,and K_(k) ^(j) is the k^(th) kernel in the j^(th) MCR component.

In one embodiment, the set of MCR components may contain two components:an inner-corner component and an outer-corner component for modeling MCReffects of inner corners and outer corners, respectively.

Note that it may be beneficial to use a set of MCR components becausethese components may also help to model other effects, e.g., etcheffects. Specifically, using the set of MCR components may provide anadditional degree of freedom during the fitting process which can helpto improve the overall accuracy of the process model.

Next, the system can identify a set of corners in the mask layout (step608).

The system can then determine a set of mask layers which includes afirst mask layer and a set of MCR mask layers (step 610). The first masklayer can include substantially all patterns in the mask layout.Further, substantially all patterns in each MCR mask layer can relate topatterns in the mask layout that are in proximity to the set of corners.Each MCR mask layer can be associated with an MCR component.

FIGS. 7A and 7B illustrate a set of mask layers in accordance with anembodiment of the present invention.

The first mask layer shown in FIG. 7A is essentially a replica of themask layout. However, the first mask layer doesn't necessarily have tocontain all patterns in the mask layout. The MCR mask layer shown inFIG. 7B contains patterns which relate to patterns in the mask layoutthat are in proximity to the set of corners. For example, FIG. 7Bcontains bevel shapes 704, 706, 708, 710, 712, and 714 that relate tothe corners in polygon 702 shown in FIG. 7A.

In one embodiment, the set of MCR layers contains two mask layers: aninner-corner mask layer and an outer-corner mask layer. Substantiallyall patterns in the inner-corner mask layer relate to patterns in themask layout that are in proximity to inner corners. Similarly,substantially all patterns in the outer-corner mask layer relate topatterns in the mask layout that are in proximity to outer corners.

FIG. 8A illustrates an outer corner mask layer in accordance with anembodiment of the present invention. The outer corner mask layercontains bevel shapes 804, 806, 810, 812, and 814 that relate to theouter corners in polygon 702 shown in FIG. 7A.

FIG. 8B illustrates an inner corner mask layer in accordance with anembodiment of the present invention. The inner corner mask layercontains bevel shape 808 that relates to the inner corner in polygon 702shown in FIG. 7A.

Although the above-described mask layers use bevel shapes, the systemmay use other shapes, e.g., notches. These mask layer patterns have beenpresented for illustration purposes and are not intended to limit thepresent invention. Accordingly, many modifications and variations willbe readily apparent to practitioners skilled in the art.

Once the mask layers have been determined, the system can determine theimproved process model by calibrating the uncalibrated process modelusing the set of mask layers and the process data (step 612).

Specifically, the system can determine the process model by fittingcoefficients in the uncalibrated process model using the process data.The fitting process can include convolving the optical component withthe mask layout or with a mask layer that contains substantially allpatterns in the mask layout. Further, the fitting process can alsoinclude convolving each MCR component with the associated MCR masklayer. Note that since the MCR layers usually do not contain patternsthat relate to 1-D (one-dimensional) regions in the mask layout, fittingthe MCR components to process data may not reduce the improved processmodel's accuracy for 1-D regions.

FIG. 9 presents a flowchart that illustrates a process for determiningan improved process model in accordance with an embodiment of thepresent invention.

The system may receive a mask layout (step 902). Next, the system mayidentify inner corners (step 904). The system may then identify outercorners (step 906).

Next, the system may select a model form (step 908). For example, thesystem may select the one-layer approach or the multi-layer approach formodeling MCR effects. Note that the system may also select a hybridapproach which uses aspects of both the one-layer approach as well asthe multi-layer approach. Specifically, a hybrid approach may modify themask layout and use a set of mask layers to model mask corner roundingeffects.

The system may then select a model corner form (step 910). For example,the system may select a bevel shape, a notch shape, or any other shapethat is appropriate for modeling MCR effects. Next, the system maycalibrate the model (step 912), and output the model (step 914).

These different options for modeling MCR effects may have differentstorage and computational requirements. For example, a process modelthat uses bevels instead of notches may be more accurate, but it mayalso increase the computational requirements for downstreamapplications. Similarly, using the multilayer approach instead of thesingle-layer approach may require more storage. Hence, to select anappropriate modeling approach, we may have to perform an analysis of thespecific constraints and requirements of a given application.

FIG. 10 illustrates a computer system in accordance with an embodimentof the present invention.

Computer system 1002 comprises processor 1004, memory 1006, and storagedevice 1008. Computer system 1002 can be coupled to display 1014,keyboard 1010, and pointing device 1012. Storage device 1008 can storeapplications 1016 and 1018, and process model 1020.

During operation, computer system 1002 can load application 1016 intomemory 1006. Next, the system can use application 1016 to determineprocess model 1020. Application 1016 can then store process model 1020on storage device 1008. The system can store a process model by storingthe parameters and/or coefficients in a computer-readable storagemedium. In one embodiment, the system may store parameters,coefficients, kernel identifiers, and information that associates theparameters and coefficients with their respective kernel identifiers. Akernel identifier can be a string that identifies a kernel, or it can bean expression that represents the kernel. The system can loadapplication 1018 into memory 1006. Application 1018 can then loadprocess model 1020 into memory 1006, and use process model 1020 todetermine a proximity correction or to predict the shape of a pattern ona photoresist layer.

FIG. 11 illustrates how a process model can be stored in accordance withan embodiment of the present invention.

User 1102 may use computer 1104 to determine a process model. Next, user1102 may store the parameters, coefficients, kernel identifiers, andinformation that associates the parameters and coefficients to thekernel identifiers on computer 1104′s hard disk or a removablecomputer-readable storage medium. Alternatively, user 1102 may store theprocess model on database 1112 which is coupled to computer 1104 vianetwork 1110. User 1106 may receive the process model from user 1102over network 1110. Alternatively, user 1106 may retrieve the processmodel from database 1112. User 1106 can load the process model oncomputer 1108 by reading the parameters, coefficients, kernelidentifiers, and the information that associates the parameters andcoefficients to the kernel identifiers.

CONCLUSION

The data structures and code described in this detailed description aretypically stored on a computer-readable storage medium, which may be anydevice or medium that can store code and/or data for use by a computersystem. This includes, but is not limited to, volatile memory,non-volatile memory, magnetic and optical storage devices such as diskdrives, magnetic tape, CDs (compact discs), DVDs (digital versatilediscs or digital video discs), or other media capable of storingcomputer readable media now known or later developed.

Furthermore, the foregoing descriptions of embodiments of the presentinvention have been presented only for purposes of illustration anddescription. They are not intended to be exhaustive or to limit thepresent invention to the forms disclosed. Accordingly, manymodifications and variations will be readily apparent to practitionersskilled in the art. Additionally, the above disclosure is not intendedto limit the present invention. The scope of the present invention isdefined by the appended claims.

1. A computer-executed method for determining a process model whichmodels mask corner rounding effects, the method comprising: receiving amask layout; receiving process data which was generated by applying aphotolithography process to the mask layout; receiving an uncalibratedprocess model which includes: an optical component; and a set ofmask-corner-rounding (MCR) components, wherein each MCR component isdesigned to model MCR effects; identifying a set of corners in the masklayout; determining a set of mask layers which includes: a first masklayer which includes substantially all patterns in the mask layout; anda set of MCR mask layers, wherein substantially all patterns in each MCRmask layer relate to patterns in the mask layout that are in proximityto the set of corners, and wherein each MCR mask layer is associatedwith an MCR component; and using one or more computers to calibrate theuncalibrated process model using the set of mask layers and the processdata.
 2. The computer-executed method of claim 1, wherein the set of MCRcomponents includes: an inner-corner component for modeling MCR effectsof inner corners; and an outer-corner component for modeling MCR effectsof outer corners.
 3. The computer-executed method of claim 1, whereinthe set of MCR mask layers includes: an inner-corner mask layer, whereinsubstantially all shapes in the inner-corner mask layer relate topatterns in the mask layout that are in proximity to inner corners; andan outer-corner mask layer, wherein substantially all shapes in theouter-corner mask layer relate to patterns in the mask layout that arein proximity to outer corners.
 4. The computer-executed method of claim3, wherein the inner-corner mask layer includes bevel shapes whichcorrespond to inner corners in the set of corners in the mask layout,and wherein the outer-corner mask layer includes bevel shapes whichcorrespond to outer corners in the set of corners in the mask layout. 5.The computer-executed method of claim 3, wherein the inner-corner masklayer includes notch shapes which correspond to inner corners in the setof corners in the mask layout, and wherein the outer-corner mask layerincludes notch shapes which correspond to outer corners in the set ofcorners in the mask layout.
 6. The computer-executed method of claim 3,wherein the inner-corner mask layer includes shapes of a first typewhich correspond to inner corners in the set of corners in the masklayout, and wherein the outer-corner mask layer includes shapes of asecond type which correspond to outer corners in the set of corners inthe mask layout, wherein the shapes of the first type are different fromthe shapes of the second type.
 7. The computer-executed method of claim1, wherein calibrating the process model includes: convolving theoptical component with the first mask layer; and convolving each MCRcomponent with the associated MCR mask layer.
 8. A computer-readablestorage device storing instructions that when executed by a computercause the computer to perform a method for determining a process modelwhich models mask corner rounding effects, the method comprising:receiving a mask layout; receiving process data which was generated byapplying a photolithography process to the mask layout; receiving anuncalibrated process model which includes: an optical component; and aset of mask-corner-rounding (MCR) components, wherein each MCR componentis designed to model MCR effects; identifying a set of corners in themask layout; determining a set of mask layers which includes: a firstmask layer which includes substantially all patterns in the mask layout;and a set of MCR mask layers, wherein substantially all patterns in eachMCR mask layer relate to patterns in the mask layout that are inproximity to the set of corners, and wherein each MCR mask layer isassociated with an MCR component; and calibrating the uncalibratedprocess model using the set of mask layers and the process data.
 9. Thecomputer-readable storage device of claim 8, wherein the set of MCRcomponents includes: an inner-corner component for modeling MCR effectsof inner corners; and an outer-corner component for modeling MCR effectsof outer corners.
 10. The computer-readable storage device of claim 8,wherein the set of MCR mask layers includes: an inner-corner mask layer,wherein substantially all shapes in the inner-corner mask layer relateto patterns in the mask layout that are in proximity to inner corners;and an outer-corner mask layer, wherein substantially all shapes in theouter-corner mask layer relate to patterns in the mask layout that arein proximity to outer corners.
 11. The computer-readable storage deviceof claim 10, wherein the inner-corner mask layer includes bevel shapeswhich correspond to inner corners in the set of corners in the masklayout, and wherein the outer-corner mask layer includes bevel shapeswhich correspond to outer corners in the set of corners in the masklayout.
 12. The computer-readable storage device of claim 10, whereinthe inner-corner mask layer includes notch shapes which correspond toinner corners in the set of corners in the mask layout, and wherein theouter-corner mask layer includes notch shapes which correspond to outercorners in the set of corners in the mask layout.
 13. Thecomputer-readable storage device of claim 10, wherein the inner-cornermask layer includes shapes of a first type which correspond to innercorners in the set of corners in the mask layout, and wherein theouter-corner mask layer includes shapes of a second type whichcorrespond to outer corners in the set of corners in the mask layout,wherein the shapes of the first type are different from the shapes ofthe second type.
 14. The computer-readable storage device of claim 8,wherein calibrating the process model includes: convolving the opticalcomponent with the first mask layer; and convolving each MCR componentwith the associated MCR mask layer.
 15. An apparatus for determining aprocess model which models mask corner rounding effects, comprising: aprocessor; and a memory storing instructions that when executed by theprocessor cause the system to determine a process model which modelsmask corner rounding effects, the instructions comprising: instructionsfor receiving a mask layout; instructions for receiving process datawhich was generated by applying a photolithography process to the masklayout; instructions for receiving an uncalibrated process model whichincludes: an optical component; and a set of mask-corner-rounding (MCR)components, wherein each MCR component is designed to model MCR effects;instructions for identifying a set of corners in the mask layout;instructions for determining a set of mask layers which includes: afirst mask layer which includes substantially all patterns in the masklayout; and a set of MCR mask layers, wherein substantially all patternsin each MCR mask layer relate to patterns in the mask layout that are inproximity to the set of corners, and wherein each MCR mask layer isassociated with an MCR component; and instructions for calibrating theuncalibrated process model using the set of mask layers and the processdata.
 16. The apparatus of claim 15, wherein the set of MCR componentsincludes: an inner-corner component for modeling MCR effects of innercorners; and an outer-corner component for modeling MCR effects of outercorners.
 17. The apparatus of claim 15, wherein the set of MCR masklayers includes: an inner-corner mask layer, wherein substantially allshapes in the inner-corner mask layer relate to patterns in the masklayout that are in proximity to inner corners; and an outer-corner masklayer, wherein substantially all shapes in the outer-corner mask layerrelate to patterns in the mask layout that are in proximity to outercorners.
 18. The apparatus of claim 17, wherein the inner-corner masklayer includes bevel shapes which correspond to inner corners in the setof corners in the mask layout, and wherein the outer-corner mask layerincludes bevel shapes which correspond to outer corners in the set ofcorners in the mask layout.
 19. The apparatus of claim 17, wherein theinner-corner mask layer includes notch shapes which correspond to innercorners in the set of corners in the mask layout, and wherein theouter-corner mask layer includes notch shapes which correspond to outercorners in the set of corners in the mask layout.
 20. The apparatus ofclaim 17, wherein the inner-corner mask layer includes shapes of a firsttype which correspond to inner corners in the set of corners in the masklayout, and wherein the outer-corner mask layer includes shapes of asecond type which correspond to outer corners in the set of corners inthe mask layout, wherein the shapes of the first type are different fromthe shapes of the second type.
 21. The apparatus of claim 15, whereinthe instructions for calibrating the process model includes:instructions for convolving the optical component with the first masklayer; and instructions for convolving each MCR component with theassociated MCR mask layer.